A.S. Convergence Rate and Lp-Convergence of Bisexual Branching Processes in a Random Environment and Varying Environment

被引：0

作者：

Sheng XIAO ^{[1
]}

Xiang-dong LIU ^{[1
]}

Ying-qiu LI ^{[2
,3
]}

机构：

[1] School of economics, Jinan University

[2] School of Mathematics and Statistics, Changsha University of Science and Technology

[3] Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology

来源：

Acta Mathematicae Applicatae Sinica | 2023年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

D O I：

暂无

中图分类号：

O211.65 [分支过程];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let(Zn) be a supercritical bisexual branching process in a random environment ξ. We study the almost sure(a.s.) convergence rate of the submartingale ■ = Zn/In to its limit ■, where(In) is an usually used norming sequence. We prove that under a moment condition of order p ∈(1, 2), ■-■ = o(e-na) a.s. for some a > 0 that we find explicitly; assuming the logarithmic moment condition holds, we have ■-■ = o(n-α)a.s.. In order to obtain these results, we provide the Lp-convergence of(■); similar conclusions hold for a bisexual branching process in a varying environment.

引用

页码：337 / 353

页数：17

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